Multi-Absorbing Phase-Type Distributions for Right-Censored Competing Risks Data

Zhihao Qiao; Budhi Surya; Azam Asanjarani; Yoni Nazarathy

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arXiv · 2609.19921

Multi-Absorbing Phase-Type Distributions for Right-Censored Competing Risks Data

Zhihao Qiao·Budhi Surya·Azam Asanjarani·Yoni Nazarathy

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Abstract

Phase-type (PH) distributions are versatile semi-parametric models for lifetime duration and can be used in survival and reliability analysis. In this paper we put forward methods and software for using PH distributions in a competing-risks model. The resulting multi-absorbing phase-type (MAPH) distribution records both the time until absorption and its cause. After formulating basic properties of this family, we develop an EM algorithm for parameter inference from exact event-time/cause observations and independently right-censored observations. For a censored subject, the E-step conditions on survival up to the censoring time and imputes both the latent transient path and its eventual cause of absorption; closed-form cause-resolved sufficient-statistic expectations are obtained from matrix exponentials. We illustrate applications and numerical properties and describe two accompanying Julia packages, in which both the exact-event and the censored E-step are implemented. Applied to intensive-care length-of-stay data in full, censored records included, the method attains a higher likelihood than the phase-type competing-risks fit previously published for those data.

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Zhihao Qiao, Budhi Surya, Azam Asanjarani, Yoni Nazarathy. 2026-09-17. Multi-Absorbing Phase-Type Distributions for Right-Censored Competing Risks Data. https://arxiv.org/abs/2609.19921

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